The Determination of Distances between Images by de Rham Currents Method
https://doi.org/10.18255/1818-1015-2020-1-96-107
Abstract
The goal of the paper is to develop an algorithm for matching the shapes of images of objects based on the geometric method of de Rham currents and preliminary affine transformation of the source image shape. In the formation of the matching algorithm, the problems of ensuring invariance to geometric image transformations and ensuring the absence of a bijective correspondence requirement between images segments were solved. The algorithm of shapes matching based on the current method is resistant to changes of the topology of object shapes and reparametrization. When analyzing the data structures of an object, not only the geometric form is important, but also the signals associated with this form by functional dependence. To take these signals into account, it is proposed to expand de Rham currents with an additional component corresponding to the signal structure. To improve the accuracy of shapes matching of the source and terminal images we determine the functional on the basis of the formation of a squared distance between the shapes of the source and terminal images modeled by de Rham currents. The original image is subjected to preliminary affine transformation to minimize the squared distance between the deformed and terminal images.
Supporting agencies: This work was supported by the Russian Foundation for Basic Research, projects № 18–07–00526 and № 18–08–01284. This work was supported by the Basic Research Program of the Siberian Branch of the Russian Academy of Sciences № I.5.1., Project № 0314-2019-0020.
About the Author
Sergey N. Chukanov
Sobolev Institute of Mathematics, SB RAS
Russian Federation
Doctor of Technical Science, Professor
Russian Federation
Doctor of Technical Science, Professor
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Review
For citations:
Chukanov S.N. The Determination of Distances between Images by de Rham Currents Method. Modeling and Analysis of Information Systems. 2020;27(1):96-107. https://doi.org/10.18255/1818-1015-2020-1-96-107
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